用Transformer学习多体系统混沌集体行为，精准捕捉统计规律。
Transformer Learning of Chaotic Collective Dynamics in Many-Body Systems
- 基于自注意力机制建模长时程相关性，突破传统循环网络局限。
- 在1维半经典霍尔斯坦模型中，准确复现混沌态的统计特性与衰减尺度。
- 适合研究复杂量子系统演化、非马尔可夫动力学的科研人员参考。
从时间序列数据直接建模混沌多体系统的简化描述极具挑战：尽管微观方程为马尔可夫过程，集体可观测量却表现出强记忆性和对初值及预测误差的指数敏感性。我们证明，基于自注意力机制的Transformer框架可有效建模此类混沌集体动力学。通过选择性重加权长程时间相关性，Transformer学习到一种非马尔可夫的简化描述，克服了传统递归架构的内在限制。以一维半经典霍尔斯坦模型为例，相互作用淬火引发电荷密度波序参量的强烈非线性与混沌动力学。虽然逐点预测在长时间后必然发散，但Transformer能忠实复现混沌的统计‘气候’特征，包括时间相关性和典型衰减尺度。结果表明，自注意力机制是学习混沌多体系统有效简化动力学的强大工具。
原文摘要 · Abstract (English)
Learning reduced descriptions of chaotic many-body dynamics is fundamentally challenging: although microscopic equations are Markovian, collective observables exhibit strong memory and exponential sensitivity to initial conditions and prediction errors. We show that a self-attention-based transformer framework provides an effective approach for modeling such chaotic collective dynamics directly from time-series data. By selectively reweighting long-range temporal correlations, the transformer learns a non-Markovian reduced description that overcomes intrinsic limitations of conventional recurrent architectures. As a concrete demonstration, we study the one-dimensional semiclassical Holstein model, where interaction quenches induce strongly nonlinear and chaotic dynamics of the charge-density-wave order parameter. While pointwise predictions inevitably diverge at long times, the transformer faithfully reproduces the statistical "climate" of the chaos, including temporal correlations and characteristic decay scales. Our results establish self-attention as a powerful mechanism for learning effective reduced dynamics in chaotic many-body systems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。